Abstract
Topological Data Analysis(TDA) is a new and fast growing field in data science. TDA provides an approach to analyze data sets and derive their relevant feature out of complex high-dimensional data, which greatly improves the working efficiency in many fields. In this paper, the author mainly discusses some mathematics concepts about topology, methods in TDA and the relation between these topological concepts and data sets (how to apply topological concepts on data). The problems of TDA, mathematical algorithm using in TDA and two application-examples are introduced in this paper. In addition, the advantages, limitations, and the direction of future development of TDA are discussed.
Highlights
Topology is the branch of pure mathematics that studies the notion of shape
The problems of Topological Data Analysis (TDA), mathematical algorithm using in TDA and two application-examples are introduced in this paper
TDA is a very powerful tool in machine learning, and it can be used with machine learning methods to get better results than using a single technology
Summary
The idea behind Topological Data Analysis (TDA) is to represent complex data sets as a network of nodes and edges, and create an intuitive map based on the similarity of the data points. The author mainly discusses some mathematics concepts about topology, methods in TDA and the relation between these topological concepts and data sets (how to apply topological concepts on data). Of general graph ics can be simplified These basic triangles are called two-dimensional simple complexes, abbreviated as two-dimensional simplex, and higher-dimensional simple complexes can use triangular highdimensional analogs (so-called N-dimensional simplex; eg: three-dimensional simplex is foursided Body). These triangles must be in a certain way, either not intersecting, or the intersecting part is its common face
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